Standardized Test Prep

SAT/ACT

66. If θ theta is in Quadrant I and tan θ = 5 12 , tangent theta equals , 5 twelfths . comma what is the value of tan 4 θ 5 fraction tangent 4 theta , over 5 end fraction to the nearest
    1. 18.10
    2. 0.33
    3. 0.32
    4. − 23.90 negative , 23.90
67. If θ theta is in Quadrant I and sin θ 3 5 , sine theta . 3 fifths , comma what is an exact value of sin 2 θ ? sine 2 theta question mark
    6. 9 25 9 twenty fifths
    7. 24 25 24 over 25
    8. 6 5 6 fifths
    9. 73.7
68. A ladder rests against a building. The ladder is 14 ft long and forms an angle of 76 . 5 ° 76 . 5 degrees with the ground. Which statement is not true?
    1. The bottom of the ladder is 13.6 ft from the base of the building.
    2. The bottom of the ladder is 13.3 ft from the base of the building.
    3. The top of the ladder touches the building 13.6 ft from the ground.
    4. The ladder forms an angle of 13 . 5 ° 13 . 5 degrees with the building.
69. Which expressions are equivalent?
    1. cos θ cosine theta
    2. cos ( − θ ) cosine open negative theta close
    3. sin ( − θ ) tan ( − θ ) fraction sine . open , negative theta , close , over tangent . open , negative theta , close end fraction
       6. I and II only
       7. I and III only
       8. II and III only
       9. I, II, and III

Short Response

70. Use a half-angle identity to find an exact value of sin   67 . 5 ° . sine 67 . 5 degrees .

Mixed Review

Find each exact value. Use a sum or difference identity. See Lesson 14-6.

71. cos 405 ° cosine , 405 degrees
72. sin ( − 300 ° ) sine open negative 300 degrees close
73. tan ( − 300 ° ) tangent open negative 300 degrees close

Find the amplitude and period of each periodic function. See Lesson 13-1.

A set of data with a mean of 39 and a standard deviation of 6.2 is normally distributed. Find each value, given its distance from the mean. See Lesson 11-9.

76. +1 standard deviation
77. − 2 negative 2 standard deviations
78. +3 standard deviations

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